I am also concerned about the heat because I want to fit all the stuff in passive cooled box without airflow around.
In the same way, if the arduino is totally off, is it correct to say that there is no flow in the circuit and the voltage converter will stop heating ?
The 2nd link you posted looks like quite a sophisticated little variable power supply... you probably don't really need anything that fancy.
If heat may be an issue then avoid "linear" regulators, and look for a "switching" regulator. Try Googling "12v 5v buck converter". You need something that can handle at least 1A (1000mA), so look for 2A.
I use these that is capable of supplying 3amps and the output voltage is stable running of a 12v battery , I used others that say supply 1amp but found when I turned on relays the Arduino just rests and the lcd flickers.
Using this one in my portable battery pack that I run my laptops on for site work when they go flat, and it uses some current sensors to measure amps in and out they seem to be more stable reading and can measure the running current if 20 milliamperes
[2 Pieces DC Converter 12V to 5V 3A 15W DC Buck Converter Module, DC to DC Reduced Voltage Regulator Car Power Converter Output Power Adapter (Wires Interface) https://amzn.eu/d/hdM8M7i](2 Pieces DC Converter 12V to 5V 3A 15W DC Buck Converter Module, DC to DC Reduced Voltage Regulator Car Power Converter Output Power Adapter (Wires Interface) https://amzn.eu/d/hdM8M7i)